Finite Group Databasebeta

← #34054962

Subgroups — #34054962

Order 19072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750105C211yesmaximal, characteristic, complemented
2#23749953C211yesmaximal, characteristic, complemented
3#23749941C211yesmaximal, characteristic, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749907C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749785C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic
10#23749735C211yesmaximal, characteristic, complemented
11#23749730C211yesmaximal, characteristic, complemented
12C4×#14558723C211yesmaximal, characteristic, complemented
13C4×#14558724C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#542×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23C4×D596C2211yescharacteristic
24C4×D596C2211yescharacteristic
25#18011871—21no—
26#18011871—21no—
27#18011869—21no—
28C2×C4⋊Dic149C2211yescharacteristic
29C4⋊C4×D149—21no—
30#18011842C2211yescharacteristic
31#18011842C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011834C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#124×C149—21no—
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68#14558726—22no—
69#14558724—22no—
70#14558723—22no—
71#14558721—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558713—21no—
82#14558713—21no—
83C4×Dic149—21no—
84C4×Dic149—21no—
85C2×Q8×C149—21no—
86C2×Q8×C149C2311yescharacteristic
87C2×D4×C149—21no—
88C2×D4×C149C2311yescharacteristic
89C22×C4×C149—21no—
90C22×C4×C149C2311yescharacteristic
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149D411yescharacteristic
95C4⋊C4×C149D411yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298#4112yes—
111D596—21no—
112D596#4112yes—
113C22⋊D149—24no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—81no—
118C4×D149—24no—
119C4×D149—81no—
120C4×D149—81no—
121#11924746—21no—
122#11924746—21no—
123#11924746—21no—
124#11924746—21no—
125C23×C149—21no—
126C23×C149C2×D411yescharacteristic
127Q8×C149—21no—
128Q8×C149—21no—
129Q8×C149—81no—
130D4×C149—21no—
131D4×C149—21no—
132D4×C149—81no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—81no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2411yescharacteristic
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149C22×D411yescharacteristic
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149C2×#4111yescharacteristic
164C4×C149C2×#4111yescharacteristic
165Dic149—22no—
166Dic149—41no—
167Dic149—41no—
168C2×C149—41no—
169C2×C149—81no—
170C2×C149#52511yescharacteristic
171C2×C149#57711yescharacteristic
172C2×C149#57711yescharacteristic
173D149—42no—
174C149#312511yescharacteristic, complemented, Sylow
175#3125—1491nomaximal, Sylow
176#542D14911yescharacteristic, complemented
177#520—1491no—
178#483—1491no—
179#481—1491no—
180#476—1491no—
181#475—1491no—
182#464—1491no—
183#463—1491no—
184#452—1491no—
185#449—1491no—
186#442—1491no—
187#441—1491no—
188C4×SD16—1491no—
189C4×SD16—1491no—
190#433—1491no—
191C2×#41—1491no—
192C2×Q16—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×D8—1491no—
196C4⋊Q8C2×D14911yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D14911yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D14911yescharacteristic
203#121C2×D14911yescharacteristic
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8C2×D14911yescharacteristic
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4C2×D14911yescharacteristic
212#117—2981no—
213#117C2×D14911yescharacteristic
214C2×C4⋊C4—2981no—
215C2×C4⋊C4—1491no—
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97—1491no—
233C4×C8—1491no—
234#41—2982no—
235#41—2982no—
236C2×Q8—21no—
237C2×Q8—1491no—
238C2×Q8C22×D14911yescharacteristic
239C2×D4—21no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4C22×D14911yescharacteristic
243C22×C4—21no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4C22×D14911yescharacteristic
249Q16—2982no—
250SD16—2982no—
251SD16—2982no—
252D8—2982no—
253C2×C8—1491no—
254C2×C8—1491no—
255C2×C8—1491no—
256C2×C8—1491no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4C22⋊D14911yescharacteristic
266C4⋊C4C22⋊D14911yescharacteristic
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4C22⋊D14911yescharacteristic
277C22⋊C4C22⋊D14911yescharacteristic
278C42—21no—
279C42—2981no—
280C42—2981no—
281C42C22×D14911yescharacteristic
282C42C22×D14911yescharacteristic
283C23—21no—
284C23—2981no—
285C23C2×C22⋊D14911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—2981no—
290Q8—1492no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—2984no—
295D4—2981no—
296D4—1492no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2984no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—11921no—
308C2×C4—11921no—
309C2×C4—11921no—
310C2×C4C2×C22⋊D14911yescharacteristic
311C2×C4C2×C22⋊D14911yescharacteristic
312C2×C4C2×C22⋊D14911yescharacteristic
313C2×C4C2×C22⋊D14911yescharacteristic
314C2×C4C2×C22⋊D14911yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—2981no—
317C8—2981no—
318C8—2981no—
319C8—2981no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2982no—
327C22—5961no—
328C22—5961no—
329C22C22×C22⋊D14911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2982no—
339C4—5961no—
340C4—5961no—
341C4#41×D14911yescharacteristic
342C4#41×D14911yescharacteristic
343C2—41no—
344C2—81no—
345C2—5962no—
346C2#2375013211yescharacteristic
347C2#2375043311yescharacteristic
348C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#542×C149C2
socleC22×C149C22×D4
prime radical#23749768C2
hypercenter#542D149
hypocenterC149#3125
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23750105C2semidirect
2. #23749953C2semidirect
3. #23749941C2semidirect
4. #23749912C2semidirect
5. #23749907C2semidirect
6. #23749844C2semidirect
7. #23749837C2semidirect
8. #23749785C2semidirect
10. #23749735C2semidirect
11. #23749730C2semidirect
12. C4×#14558723C2semidirect
13. C4×#14558724C2semidirect
14. #23749686C2semidirect
15. #542×C149C2semidirect
174. C149#3125semidirect
176. #542D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237501052
#237499532
#237499412
#237499122
#237499072
#237498442
#237498372
#237497852
#237497682
#237497352
#237497302
C4×#145587232
C4×#145587242
#237496862
#542×C1492
#3125149